Where will it go? Concepts of motion in complex events

Museum of Science, BostonTemple University

Imagine a billiard ball (A) rolling across a table, hitting a second, stationary ball (B) straight on. What happens when the two balls collide? A should stop and B should roll away immediately. Most adults can accurately imagine this scenario. In fact, by six months of age infants recognize this outcome as probable and react to it differently than less probable alternatives (Cohen & Oakes, 1993; Leslie & Keeble, 1987; Oakes & Cohen, 1990).

However, the motion events that we encounter over the course of a normal day are far more complex than a single force being applied to a stationary object. Motion events typically involve multiple forces acting over a period of time on an object. For example, what would change about the event if B had also been moving? When A strikes B it will still apply a force that causes B to accelerate in the direction A was moving, but now the initial velocity of B must also be considered to determine B’s subsequent motion. This seemingly small change can result in a problem that is far more difficult.

This increase in difficulty is sufficient to create problems on which even adults frequently make mistakes (Clement, 1982; Halloun & Hestenes, 1985a, 1985b; Viennot, 1979). Adults typically have multiple naïve conceptions about motion that are not easily remedied by instruction and can last a lifetime (Halloun & Hestenes, 1985a; Viennot, 1979). Students in traditionally taught introductory physics courses typically show no change in their conceptual understanding across a wide variety of topics, even after having successfully passed their course (Halloun & Hestenes, 1985b).

These naïve conceptions about motion are not a unique result of individual experience; they are common amongst individuals and mirror common pre-Newtonian theories (Halloun & Hestenes, 1985b). In my dissertation, I treat common naïve conceptions as a window into how people learn about and understand the world. This study explores four questions about the development of conceptions of motion. First, what, if any, shared naïve conceptions do children (5.5 to 6.5 years old) hold about complex motion problems? Second, what is the general ability of children on these problems? In other words, how complex can a motion problem be for children to generally be able to solve it? Third, what features of a problem influence the application of a common naïve conception, called the dominance principle, and how does this compare across age groups? The dominance principle dictates that when two forces are combined one will win out over the other; its direction will completely determine the direction of the motion. In other words, the net force is equal to the “largest” force instead of an addition of the two. It is unclear how the “largest” force is identified. For example, dominance could be implied by both timing (i.e., more recent forces are “larger”) and size (i.e., forces with a larger magnitude are “larger”). Fourth, what role might spatial thinking play in successfully predicting the correct motion?

Method

Fifty-two adults between the ages of 18 and 65 (M=22.75 years, 27 male) and sixty children between 5.5 to 6.5 years old (M = 70.63 months, 31 male) were included in the analysis. Conceptions of complex motion events (i.e., those with multiple components of motion) were elicited through a tablet-based game involving cartoon hedgehogs blowing a ball around a game board (Figure 1 and Figure 2). The problems of interest on this game involved two forces acting on an object either in the same dimension (i.e., at 0 degrees or 180 degrees to each other) or in two dimensions. For the two dimension problems the forces acted completely orthogonally (i.e., at 90 degrees to each other) and would either act simultaneously or sequentially. Participants were also given age-appropriate measures of mental folding, mental rotation, and vocabulary (to control for general intelligence). Math measures were also given to children, but are not reported here.

Figure 1. Two forces applied to the same object, at the same time, in the same dimension. Arrows representing the two forces and the resultant motion have been added.

Figure 2. Two forces applied to the same object, sequentially, and in two different dimensions. Arrows representing the two forces and the resultant motion have been added. The temporal dominance solution is the top right square (i.e., the one directly in front of the red hedgehog).

Participants were classified as having a conception if at least 5 out of every 6 responses conformed to a pattern. A lack of this degree of consistency does not necessarily indicate that a participant was guessing, though some likely were. Rather, classification of not having a conception indicates either some degree of not being sure how to respond or changing strategies partway through the test. Participants who were able to self-correct their conceptions as the test progressed were unavoidably included in this group.

There was strong evidence that conceptions of motion are still developing between 5.5 and 6.5 years of age; unlike most adults, the majority of children’s patterns of responses were not consistent with having a conception. However, of the children who did show evidence of a conception, the most common response was the same naïve conception seen in adults. This shared conception (i.e., the most common response, in all age groups, when a consistent error was made) was “temporal dominance.” Temporal dominance is the belief that the most recently applied force, rather than the one with the largest magnitude, would determine the motion of an object. Somewhat surprisingly, there was also evidence that a new misconception arises with age (i.e., that applying a force to a moving object that is perpendicular to its motion will cause it to slow down).

While children generally demonstrated misconceptions or inconsistent responses to two-dimension problems, they also demonstrated a general ability to successfully reason about complex motion problems when limited to a single dimension. Young children, 5.5 to 6.5 years old, are already capable of thinking about how different components of motion might combine. These results replicate those found in Göksun, George, Hirsh-Pasek, and Golinkoff (2013). Interventions aimed at improving qualitative understanding of complex motion events could therefore begin as children are first entering formal schooling. Early intervention may be particularly important to help address sex differences commonly found in adults.

The results suggest that there is a developmental trajectory for a person’s conceptions of motion, one in which educators may be able to intervene. However, there does not appear to be a single trajectory common to all children. Some children develop early and can succeed at the task. Others show the temporal dominance pattern – a complex, though inaccurate, conceptualization of the motion that is fairly close to the truth and is common amongst adults. Still others have yet to develop the conceptions they are likely to hold as adults. While there may be shared developmental trajectories between males and females, each group must also contain unique trajectories.

Mental folding, but not mental rotation was found to predict performance on problems that involved multiple components, but only when they were acting in a single dimension and only for children. This result does not necessarily suggest that spatial thinking would not be helpful for adults on these problems. Rather, it may be that adults have entrenched misconceptions that discourage them from considering the problem anew by relying on their spatial thinking skills. It is unclear why mental folding, but not mental rotation was correlated with successfully solving one-dimension problems. The difference may lie in the fact that mental rotation is a rigid transformation (i.e., the distance between all points within the object is preserved) and mental folding is not. A fold creates two distinct regions and the relation between them must be maintained within the context of the larger whole. Similarly, applying two forces two an object creates two distinct components of motion and the relation between them must be considered to understand the single resultant motion that will occur. Spatial thinking strategies should be considered for any intervention with children in this age group.